Make a blender material dull
Thats actually not a reflection but indirect light.
you can use a light path node (more info on the node here) to control the color of your cube before and after light hits it.
Here is a basic node setup for your cube material:

the upper color of the mix color node controls the color of the light after it bounces off of the cube. the other color is the color of your cube itself.
Before

After